Buhong Zheng

Aggregate Poverty Measures

The way poverty is measured is important for an understanding of what has happened to poverty as well as for anti-poverty policy evaluation. Sens (1976) pathfinding work has motivated many researchers to focus on the way poverty should be measured. A poverty measure, argued by Sen, should satisfy certain properties or axioms and the desirability of a poverty measure should be evaluated by these axioms. During the last two decades, many researchers have adopted the axiomatic approach pioneered by Sen to propose additional axioms and develop alternative poverty measures. The objective of this survey is to provide a clarification on the extensive literature of aggregate poverty measures. In this survey, we first examine the desirability of each axiom, the properties of each poverty measure, and the interrelationships among axioms. The desirability of an axiom cannot be evaluated in isolation, and some combination of axioms may make it impossible to devise a satisfactory poverty measure; some axioms can be implied by other axioms combined and so are not independent; some others are ad hoc and are disqualified as axioms for poverty measurement. Based on the interactions among axioms, we identify the ‘core’ axioms which together have a strong implication on the functional form of a poverty measure. We then review poverty measures that have appeared in the literature, evaluating the interrelationships among different measures, and examining the properties of each measure. The axioms each measure satisfies/violates are also summarized in a tabular form. Several ‘good’ poverty measures, which have not been documented by previous surveys, are also included.

Mobility measurement,transition matrices and statistical inference

This paper develops statistical inference procedures for testing income mobility with transition matrices. Both summary mobility measures and partial mobility orderings are considered. We first examine the different ways that transition matrices are constructed in the literature on mobility measurement. Different approaches lead not only to distinct interpretations of mobility but also to different sampling distributions. The large sample properties of the estimates of transition matrices allow us to derive testing procedures for both summary mobility measures and partial orders of mobility across income regimes. The tests are illustrated by applying them to income mobility in the U.S. and Germany using the Panel Study of Income Dynamics and German Socio-Economic Panel data.

Envy, malice and Pareto efficiency: An experimental examination

Abstract Economists have long speculated that envy and malice play important roles in economic decisions. Surprisingly little empirical evidence has been offered in support of such claims. This paper uses experimental and multinomial logit techniques to estimate the effects of envy and malice in economic decisions involving Pareto efficiency. Envy and malice turn out to be powerful motivations with strong differential impacts across countries and relative positions. In some cases, opposition to Pareto gains reaches 60%. Behind a veil of ignorance, however, opposition falls to 10% overall. Pareto efficiency thus garners its greatest support under conditions which can lay claim to greatest legitimacy, those free of situational and personal bias.“... the greater part of human actions have their origin not in logical reasoning but in sentiment. This is particularly true for actions that are not motivated economically.... Man, although impelled to act by nonlogical motives, likes to tie his actions logically to certain principles; he therefore invents these a posteriori in order to justify his actions.”V. Pareto in The rise and fall of the elites (1968, p. 27)

Statistical inference for poverty measures with relative poverty lines

Relative poverty lines such as one-half median income have been increasingly used in poverty studies. This paper contributes to the literature by developing statistical inference for testing decomposable poverty measures with relative poverty lines. The poverty lines we consider are percentages of mean income and percentages of quantiles. We show that the estimates of poverty indices with relative poverty lines are asymptotically normally distributed and that the covariance structure can be consistently estimated. As a consequence, asymptotically distribution-free statistical inference can be established in a straightforward manner.

Measuring Lifetime Poverty

This paper presents an axiomatic framework for measuring lifetime poverty over multiple periods. For an individual, we argue that lifetime poverty is influenced by both the “snapshot” poverty of each period and the poverty level of the “permanent” lifetime consumption; it is also influenced by how poverty spells are distributed over the lifetime. We axiomatically characterize classes of lifetime poverty indices and derive dominance conditions of poverty orderings for both individual and societal lifetime poverty measurements.

Unit-Consistent Decomposable Inequality Measures

This paper introduces a new axiom-the unit consistency axiom-into inequality measurement. This new axiom requires the ordinal inequality rankings (rather than the cardinal indices) to be unaffected when incomes are expressed in different units. I argue that unit consistency is an indispensable axiom for the measurement of income inequality. When unit consistency is combined with decomposability, I show that the unit-consistent decomposable class of inequality measures is a two-parameter extension of the one-parameter generalized entropy class. The extended class accommodates a variety of value judgments and includes different types of inequality measures. Copyright (c) The London School of Economics and Political Science 2006.

Statistical Inference and the Sen Index of Poverty

Statistical inference procedures are developed for A. K. Sens distribution-sensitive index of poverty and each of its components--the headcount ratio, income gap ratio, and the Gini index of the poor. Using results from U-statistics, the authors show that estimates of the index and its components all have a jointly asymptotically normal distribution and the variance-covariance structure can be consistently estimated. The inference tests are illustrated by applying them to the same microeconomic data set used in estimating official U.S. poverty statistics. The application reveals that the Sen index increased significantly in each of the three periods considered. Copyright 1997 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

An axiomatic characterization of the Watts poverty index

Abstract Although the first distribution-sensitive, decomposable poverty index, the Watts index has long been neglected by the profession even when it was searching for a decomposable index. This neglect is due partly to the lack of an axiomatic characterization for the Watts index. This paper adopts an axiomatic approach and complements the Watts index with such a characterization. Under a set of reasonable axioms, the Watts index is the unique index if a poverty index is perceived as the absolute amount of social welfare loss due to poverty. The Watts index is relatively easy to apply. It also satisfies all basic axioms for a good poverty index.

On the consistent measurement of attainment and shortfall inequality.

In measuring inequality of a bounded variable such as health status, one can focus on attainments or shortfalls. However, rankings of social states by attainment and shortfall inequality do not necessarily mirror one another. We propose a requirement, that attainment inequality and shortfall inequality be measured consistently, and we examine the performance of partial orderings and indices of inequality in this respect. For relative inequality and all currently documented intermediate inequality concepts, the orderings fail our consistency requirement, as do all indices which respect these orderings. However, the absolute inequality partial ordering satisfies consistency. We identify two classes of indices of absolute inequality, one containing rank-independent and the other rank-dependent indices, which measure attainment and shortfall inequality consistently (in fact identically). The only subgroup decomposable inequality index, of any type, which measures attainment and shortfall inequality consistently is the variance. We discuss implications for the study of pure health inequality.

Inference Tests for Gini-Based Tax Progressivity Indexes

Distribution-free statistical inference procedures for changes in Lorenz- and Gini-based indexes of tax progressivity are developed and applied. Related but distinct tests for the Reynolds–Smolensky index of residual progression and the Kakwani index of liability progression are provided. The inference procedures are illustrated by applying them to Luxembourg Income Study microdata for Sweden, the United Kingdom, and the United States before and after periods of tax reform. In each country a finding of significant change depends on the choice among progressivity indexes. No single index exhibits a consistent pattern of significant change in all countries across time.